Strand Debonding for Pretensioned Girders (2017)

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52 3.1 Research Approach The effects of strand debonding on the performance of prestressed girders were examined experimentally through design, fabrication, and testing of six girders. The data obtained at pre- stress release and at various stages of load testing were utilized for this purpose. The FEM plat- form described in Section 2.4 and STM discussed in Section 2.5 were utilized to develop a better understanding of the experimental data. 3.2 Design and Detailing of Test Specimens Both ends of six full-scale girders were tested for a total of 12 sets of results. The main test vari- ables were (1) girder shape (single-web, box, or U), (2) amount of debonding of partially debonded strands, (3) concrete strength, and (4) strand diameter. Each girder had different debonding ratios at ends A and B. Key aspects of the specimens are summarized in Table 3.1. The specimen details are shown in Appendix E. With the exception of AASHTO BI-36, all the girders had a 6-in. thick slab over the entire width of the top flange. The deck slab reinforcement was designed according to the empirical design procedure described in AASHTO LRFD Article 9.7.2.5. No slab was pro- vided on the BI-36 girder; additionally, a 2.5-ft. thick end diaphragm was provided to replicate a common practice used in box girders. The test girders were designed and detailed to satisfy the following criteria: a. Satisfy concrete tensile stress limits at prestress release (AASHTO LRFD Article 5.9.4.1.2). b. Check AASHTO LRFD Eq. 5.8.3.5-2 from the interior face of support to the critical section to ensure that there is adequate Aps fps, accounting for debonding. As debonded strands become bonded, their pretensioning force is gradually developed. Figure 3.1 compares transfer of pretensioning forces in a girder with bonded and partially debonded strands. In this representative case, the full capacity of all strands in the section, Aps fps, is not available before 21 ft into the span. The calculations were based on the current AASHTO-prescribed equation for strand development length: 2 3 [5.11.4.2.1]l f f dd ps pe b= κ −     The depths of the test girders were greater than 24 in.; hence, the value of k was taken as 1.6 for fully bonded strands. (The value of k would have been 1.0 had the girders been shallower than 24 in.) For the partially debonded strands, a value of 2.0 was used for k. Experimental Research Approach, Findings, and Associated Analytical Simulations C h a p t e r 3

experimental research approach, Findings, and associated analytical Simulations 53 Table 3.1. Key details of the test specimens. Girder db(in.) End Total No. of Strands Debonding Ratio Reinforcement Total Per Row 0 to 3' 3 to 6' 6 to 9' 9 to 12' >12' Longitudinal Transverse (No. 4) No. & Size Cutoff Point (ft) Web Bottom flange U shaped AASHTO BI-36 0.5 A Row1: 15 Section 0.50 0.36 0.18 0.09 0 4 No. 6 8.5 @ 12 in. (outside of end diaphragm) 2 spaces @ 3 in.Row 1 0.40 0.27 0.13 0 0 Row 2 0.71 0.57 0.29 0.29 0 7 spaces @ 6 in. B Row2: 7 Section 0.18 0.09 0 0 0 None N/A Row 1 0.13 0 0 0 0 @ 12 in. to midspan Row 2 0.29 0.29 0 0 0 AASHTO BT-54 0.6 A Row1: 10 Section 0.60 0.40 0.20 0 0 2 No. 6 6.5 4 spaces @ 3 in. 8 spaces @ 3 in.Row 1 0.40 0.40 0 0 0 8 No. 6 13.5 Row 2 0.80 0.40 0.40 0 0 10 spaces @ 6 in. B Row2: 10 Section 0.10 0 0 0 0 6 No. 6 6.5 @ 18 in. to midspan Row 1 0.20 0 0 0 0 @ 18 in. to midspan Row 2 0.00 0 0 0 0 AASHTO Type III-a 0.5 A Row1: 8 Section 0.50 0.25 0.13 0 0 2 No. 5 5.5 3 spaces @ 3 in. 3 spaces @ 3 in.Row 1 0.25 0 0 0 0 6 No. 5 10.5 Row 2 0.75 0.50 0.25 0 0 10 spaces @ 6 in. B Row2: 8 Section 0.25 0.13 0 0 0 2 No. 5 6.5 @ 18 in. to midspan Row 1 0.25 0 0 0 0 4 No. 5 9.5 @ 18 in. to midspan Row 2 0.25 0.25 0 0 0 AASHTO Type III-b 0.5 A Row 1: 8 Section 0.56 0.33 0.11 0 0 2 No. 5 5.5 3 spaces @ 3 in. 3 spaces @ 3 in.Row 1 0.25 0 0 0 0 6 No. 5 10.5 Row 2 0.80 0.60 0.20 0 0 10 spaces @ 6 in. B Row 2: 10 Section 0.22 0.11 0 0 0 4 No. 5 5.5 @ 18 in. to midspan Row 1 0.25 0 0 0 0 4 No. 5 9.5 @ 18 in. to midspan Row 2 0.20 0.20 0 0 0 Nebraska NU-1100 0.7 A Row 1: 18 Section 0.45 0.27 0.18 0.09 0 6 No. 6 5.5 3 spaces @ 3 in. 3 spaces @ 3 in.Row 1 0.44 0.33 0.22 0.11 0 Row 2 0.50 0 0 0 0 10 spaces @ 6 in. B Row 2: 4 Section 0.27 0.18 0.18 0.18 0 4 No. 6 5.5 @ 12 in. to midspan Row 1 0.33 0.22 0.22 0.22 0 @ 12 in. to midspan Row 2 0.00 0 0 0 0 Texas U-40 0.6 A Row 1: 19 Section 0.50 0.35 0.19 0 0 22 No. 6 14.5 3 spaces @ 3 in. 3 spaces @ 3 in.Row 1 0.42 0.21 0 0 0 Row 2 0.71 0.71 0.71 0 0 22 spaces @ 4 in. 22 spaces @ 4 in. B Row 2: 7 Section 0.23 0.15 0.08 0 0 16 No. 6 13.5 Row 1 0.21 0.11 0 0 0 @ 6 in. to midspan @ 6 in. to midspan Row 2 0.29 0.29 0.29 0 0 Note: db = strand diameter. c. Check AASHTO LRFD Eq. 5.8.3.5-1 elsewhere along span to ensure that there is adequate Aps fps, accounting for debonding. d. Provide longitudinal nonprestressed reinforcement (i.e., added As fy) per AASHTO LRFD Article 5.8.3.5 if the checks in b or c are not satisfied. e. Follow the detailing rules summarized in Table 3.2. 3.3 Material Properties The experimentally determined concrete strengths (AASHTO Method T22) and material properties for all the reinforcing bars (AASHTO Method T244) are summarized in Tables 3.3 and 3.4, respectively. The concrete mix designs are provided in Appendix F. All seven-wire pre- stressing strand used was 270 ksi low-relaxation strand.

54 Strand Debonding for pretensioned Girders 3.4 Transfer Length During fabrication of the girders, five vibrating wire strain gages were placed in the concrete near the centroid of the strands at each end of each girder. The strains measured by these gages were used to assess the in situ transfer lengths, which were compared with computed values. The strain at each point along the girder length was determined by dividing the calculated stress by the calculated modulus of elasticity of concrete at prestress transfer. The concrete compressive stresses at the elevation of the vibrating wire gages (compression is negative) were calculated based on both the gross section (Eq. 3.1) and transformed section properties (Eq. 3.2). Eq. 3.1, , , , f P A Pe y y I M y y I c g e g g c g g sw c g g ( ) ( ) = − − − + − Figure 3.1. Development of pretensioning force in girders with partially debonded strands. Table 3.2. Detailing rules used for the test girders. AASHTO BT-54, AASHTO Type III, and Nebraska NU-1100 o Do not debond more than 50% of the bottom row strands. o Keep the outermost strands in all rows located within the full-width section of the flange (shaded region) bonded. Full width is understood to mean the full width of the bottom flange less a distance accounting for the chamfer—typically 2 in. on both sides. o With the exception of the outermost strands, debond strands further from the section vertical centerline preferentially to those nearer the centerline. AASHTO BI-36 and Texas U-40 o Do not debond more than 50% of the bottom row strands. o Keep the strands located in the planes of the webs bonded. All girders o Follow AASHTO LRFD Article 5.11.4.3: Not more than 40 percent of the debonded strands, or four strands, whichever is greater, shall have the debonding terminated at any section. o Provide splitting resistance according to AASHTO LRFD Article 5.10.10.1. o Provide confinement reinforcement according to AASHTO LRFD Article 5.10.10.2. o Satisfy the requirements proposed in Section 4.2 of the report.

experimental research approach, Findings, and associated analytical Simulations 55 Eq. 3.2, , , , f P A Pe y y I M y y I c transformed e transformed transformed c transformed transformed sw c transformed transformed ( ) ( ) = − − − + − As shown schematically in Figure 3.2, P is introduced in the girder bulb but it is some distance into the girder, xf , before the entire cross-sectional area is engaged in resisting P. That is, Ae,g = Abulb or Ae,transformed = Abulb,transformed at x = 0, and Ae,g = Ag and Ae,transformed = Atransformed at x = xf . Distance xf is defined by the assumed load-spreading angle, described by q in Figure 3.2. Angle q is taken as 30°, which approximately corresponds to a 2:1 strut angle typically assumed in D regions. In the transformed section calculations, the staggered bonding of the prestressing strand and the presence of the nonprestressed reinforcement were taken into account. Moreover, “voids” in the section representing unbonded strands were incorporated. The effective prestressing force (P) was computed by accounting for elastic shortening deter- mined based on AASHTO LRFD Article 5.9.5.2.3a-1 evaluated at each section. The transfer Table 3.3. Measured concrete strengths (ksi). Girder End At Release, f’ci Age at Test (days) f’c at Test Slab at Time of Test AASHTO BI-36 A 7.4 102 12.6 N/A B 97 12.2 AASHTO BT-54 A 10.2 42 17.4 11.4* B 18 15.2 11.2* AASHTO Type III-a A 6.9 93 12.6 7.4 B 78 12.2 6.2 AASHTO Type III-b A 8.3 184 13.8 6.1 B 155 13.2 5.7 Nebraska NU-1100 A 8.4 67 14.0 6.9 B 41 13.2 6.1 Texas U-40 A 6.9 110 12.8 5.9 B 95 12.0 5.8 *Due to scheduling issues, it was necessary to achieve at least 6 ksi in 7 days. Therefore, the deck slab was cast using a mix design that is typically used for prestressed girders. Girder Bar Size fy (ksi) fu (ksi) u AASHTO BI-36 No. 3 82.1 120 0.126 No. 4 72.7 112 0.128 No. 6 65.4 102 0.186 AASHTO BT-54 No. 4 69.7 107 0.127 No. 6 65.9 106 0.132 AASHTO Type III-a No. 4 63.6 100 0.191 No. 5 75.6 113 0.159 AASHTO Type III-b No. 4 63.6 100 0.191 No. 5 75.6 113 0.159 Nebraska NU-1100 No. 3 75.1 101 0.238 No. 4 79.0 106 0.254 No. 5 70.1 103 0.128 No. 6 69.2 109 0.120 Texas U-40 No. 4 70.5 110 0.157 No. 5 67.1 105 0.093 No. 6 67.6 110 0.145 Table 3.4. Measured material properties of reinforcing bars.

56 Strand Debonding for pretensioned Girders length was taken either as 60db (db = strand diameter) per AASHTO LRFD Bridge Design Speci- fications or the value obtained from Eq. 3.3 (NCHRP Report 603: Ramirez and Russell 2008). In this equation, f ′ci is the concrete strength at release, summarized in Table 3.3. The resulting calculated transfer lengths are provided in Table 3.5. l d f dt b ci b 120 40 Eq. 3.3= ′ ≥ The stress determined from Eq. 3.1 or Eq. 3.2 was divided by the concrete modulus of elastic- ity at prestress transfer (Eci) to obtain the predicted concrete strain (ec); these strains are com- pared with the measured values. The value of Eci was determined from Eq. 3.4, which has been published in the 2015 edition of AASHTO LRFD Bridge Design Specifications. E K w fc c c120,000 Eq. 3.41 2.0 0.33= ′ The value of K1 was taken as 1.0 for all the girders with the exception of Nebraska NU-1100 for which 0.85 was used (Larson et al. 2009). The value of f ′c was set equal to f ′ci (concrete strength at release), and 0.145 kcf was used for wc. The calculated and measured strains are compared in Figure 3.3. Following common practice, the effects of the end diaphragms (blocks) in girder BI-36 were neglected. The gross section prop- erties (area and moment of inertia) are smaller than their counterparts computed from trans- formed section properties. Hence, the strains based on gross section properties are, expectedly, higher than those calculated from transformed section properties. With the exception of the Texas U-40 girder, the trend of the measured data is captured reasonably well. Finite element modeling will be presented in Section 3.7.2.2 to interpret the data for Texas U-40. At some locations and Table 3.5. Release concrete strengths and calculated transfer lengths. Girder f’ci (ksi) db (in.) Calculated Transfer Lengths (in.) AASHTO (60db) NCHRP 603 (Eq. 3.3) AASHTO BI-36 7.4 0.5 30 22 (44db) AASHTO BT-54 10.2 0.6 36 24 (40db) AASHTO Type III-a 6.9 0.5 30 23 (46db) AASHTO Type III-b 8.3 0.5 30 21 (42db) Nebraska NU-1100 8.4 0.7 42 29 (41db) Texas U-40 6.9 0.6 36 27 (45db) Figure 3.2. Transition of cross-sectional area from the bulb area to the girder area.

experimental research approach, Findings, and associated analytical Simulations 57 Figure 3.3. Measured and computed longitudinal concrete strains at soffit. (c) AASHTO Type III-a (b) AASHTO BT-54 (a) AASHTO BI-36 (continued on next page)

58 Strand Debonding for pretensioned Girders Figure 3.3. (Continued). (e) Nebraska NU-1100 (f) Texas U-40 (see Section 3.7.2.2 for additional evaluation) (d) AASHTO Type III-b

experimental research approach, Findings, and associated analytical Simulations 59 for some of the girders, the calculations based on the current AASHTO transfer length cor- relate better with experimental data, whereas the transfer length recommended in NCHRP Report 603 (Ramirez and Russell 2008) yields more accurate results for some other cases. No clear conclusion can, therefore, be made about the accuracy of either transfer length calcula- tion method. For the majority of cases, the measured strains are larger than the computed values. The friction between the form and girder, which is not reflected in the calculations, would affect the boundary conditions, and, hence, the level of compressive strain in the con- crete to a small degree. 3.5 Testing Program The two ends of each girder (End A and End B), which had different amounts of strand debonding, were tested separately. In each case End B was tested first. The test specimens were extensively instrumented to capture key behavior. The test setups and instrumentation are sum- marized in this section. 3.5.1 Test Setup The girders were supported on neoprene pads similar to those typically used in construction. For single-web girders, full-flange width pads, having a thickness of 1.375 in. were provided for all the girders except for BT-54, in which 22 in. of 24.5 in. bottom flange width was supported. For AASHTO BI-36, two 9-in. wide by 3-in. thick neoprene pads were placed under each web. Two 3-in. thick neoprene pads were also placed under each web of Texas U-40. These pads engaged the outer 7-in. width of the bottom flange. During testing of End B of Texas U-40, a third pad had inadvertently been installed at the middle of the soffit at both ends. After a total load of 120 kips, the girder was unloaded, the middle pads removed, and testing resumed. Only two pads, one under each web, were placed at each end when End A was tested. The data pre- sented for the Texas U-40 herein are for the second loading of End B with only the two outer pads in place. The lengths of the pads under the soffit were 12 in. for all the girders. Displacement transducers were attached to the girder to measure the compression of pads during testing so the beam deflections could be corrected for this movement. A single concentrated load was used to test the girders. The location of the load was selected such that the shear span-to-depth ratio (a/dv) would not be less than 2.0 in order to prevent direct transfer of the load to the support through arching action. The values of a/dv are sum- marized in Table 3.6. Each end was tested separately with End B tested first. After testing End B, the girder was repositioned in order to test End A, which had a larger debonding ratio than End B. With the exception of Texas U-40, which was tested as a simply supported span, testing of each end con- sisted of a simple span with a propped cantilever overhang, as shown in Figure 3.4. To prevent cracking due to the self-weight of the cantilevered portion, an air jack was used to prop the end of the girder. The air pressure was calibrated such that the force in the jack actively compensated for the self-weight of the cantilevered portion throughout the duration of the test; thus, the girder was effectively tested as a simply supported span. At the conclusion of testing End B of AASHTO BT-54, a number of minor cracks were found to have extended into the span of End A (see Figure 3.5). In order to mitigate the effects of these cracks, the girder was vertically post-tensioned as shown in Figure 3.6 before testing End A. The total applied post-tensioning force of 120 kips was sufficient to close the small cracks. Table 3.6. Shear spans and shear span-to- depth ratios. Girder a (ft) a/dv AASHTO BI-36 5.00 2.73 AASHTO BT-54 10.0 2.34 AASHTO Type III-a 7.75 2.15 AASHTO Type III-b 7.75 2.16 Nebraska NU-1100 7.75 2.20 Texas U-40 7.75 2.39

Figure 3.4. Loading arrangements. (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a, AASHTO Type III-b, and Nebraska NU-1100 End A P (ii) Testing of End A Air jack End B P (i) Testing of End B Air jack 5'24'10' 6" 10' 6"5' 24' End A Air jack 34' 55' P End B Air jack 20' 5" 55' 10'34' P 20' 6" 10' (i) Testing of End B (ii) Testing of End A 7' 9" 39' End B End A P P (i) Testing of End B (ii) Testing of End A Air jack Air jack 7' 9" 55' 15' 6" 39' 15'6 " (d) Texas U-40 7' 9" 32' 31' 7' 9" 32' 31' (i) Testing of End B (ii) Testing of End A P P

experimental research approach, Findings, and associated analytical Simulations 61 3.5.2 Instrumentation During fabrication of the girders, a number of electrical resistance strain gages were bonded to transverse and longitudinal reinforcing bars. Moreover, a number of electrical resistance strain gages were bonded to the second-layer strands before casting AASHTO BT-54, AASHTO Type III-a, and AASHTO Type III-b. After the girders were delivered to the University of Cincinnati Large Scale Test Facility, additional strain gages were bonded to a number of the strands. These additional gages were applied within small “knockouts” left in the girders dur- ing concrete placement in a procedure used for all specimens tested in this program. At each end, six strain gages were bonded to the concrete surface to monitor compressive strain near the top of the bridge deck. Five vibrating wire gages were placed in the concrete near the centroid Figure 3.5. Extension of cracking into End A span in AASHTO BT-54. Figure 3.6. Post-tensioning of cracked end before testing End A of AASHTO BT-54.

62 Strand Debonding for pretensioned Girders of the strands at each end. The locations and numbers of strain gages are summarized in Appendix G. The test specimens were externally instrumented to measure the slip of a number of bonded and debonded strands (the locations at which the slips were measured are provided in Appendix G), average shear deformation within the shear span, and the deflection at the load point. The vertical displacement of the girder at the center of each support was measured in order to account for the deformation of the neoprene pads. A calibrated pressure transducer was used to monitor the applied load from the hydraulic rams. 3.5.3 Test Results and Discussions With the exception of Nebraska NU-1100 and End B of Texas U-40, all the specimens were loaded to failure. Total failure at End B of Texas U-40 would have compromised, if not effec- tively prevented, the testing of End A. Therefore, End B of this girder was loaded to only its pre- dicted capacity, which will be discussed in Section 3.5.3.1. It was deemed unsafe to load the Nebraska NU-1100 girder, having 22 0.7-in. diameter strands, to failure considering the amount of energy that would have been released in the event of a catastrophic failure. This girder, there- fore, was loaded to only slightly above its predicted capacity. 3.5.3.1 Capacity, Stiffness, and Failure Mode The strains measured by the vibrating wire gages were used to infer the magnitude of prestress loss. The total losses ranged between 3% for Texas U-40 and 11% for Nebraska NU-1100. These values, in conjunction with the measured material properties, were used to calculate the expected capacity of each specimen per AASHTO LRFD Bridge Design Specifications (see Appendix H). In the calculations, the resistance factors were taken as unity since the test girders were cast under controlled conditions, the loading was well defined and known a priori, and the purpose of the calculation was to determine a predicted capacity, not a design load. The measured loads (and shears) were normalized with respect to the calculated capacities of each girder. The measured deflections were normalized with respect to the deflection measured at the calculated capacity. The resulting normalized load-deflection responses are illustrated in Figure 3.7. Table 3.7 com- pares the normalized peak loads and normalized deflections at peak load for End A and End B. In each case, End B met the current AASHTO limits on the amount of debonding, while End A exceeded these limits. Based on the presented results, the following observations are made: 1. All the specimens successfully developed their predicted capacities. The failure loads were at least 43% larger than the nominal capacities (no reduction factors) calculated based on the measured material properties and inferred prestress loss. The normalized failure loads were on the order of 20% greater when determined based on AASHTO LRFD Bridge Design Speci- fications and nominal material properties. The large amounts of debonding at End A were not detrimental to the expected load-carrying capacity of the girders. 2. With the exception of AASHTO BI-36, the normalized deflections at peak load for End A and End B are comparable. The normalized load-deflection for AASHTO BI-36 [Figure 3.7(a)] clearly illustrates that End A of this girder achieved its peak capacity at a larger deflection. 3. At peak load, which corresponds to failure if the specimen were loaded to its ultimate capac- ity, the deflection was at least 2.3 times that when the predicted capacity was developed. The large amounts of debonding did not negatively impact the “ductility” inherent in the pre- stressed girders. 4. The slopes of the normalized load-deflection relationships at End A and End B are essentially the same up to developing the predicted capacities (i.e., when the value of the normalized load is equal to 1). The larger amount of debonding at End A did not have a noticeable effect

experimental research approach, Findings, and associated analytical Simulations 63 on the overall stiffness of the girders. This observation should be expected, as the relatively small area of prestressing reinforcement does not affect the stiffness; and debonding, which is localized near the girder ends, has little or no effect on deflection. The failure patterns of the girders loaded to their ultimate capacity are summarized in Fig- ure 3.8. Based on these photographs, the failure modes were characterized as noted in this figure. The Nebraska NU-1100 and End B of Texas U-40 were not loaded to failure. The dowel action at End A of AASHTO Type III-b (shown in Figure 3.9) is believed to account for the residual strength following the initial loss of carrying capacity that is apparent in Figure 3.7(d). (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a (d) AASHTO Type III-b (e) Nebraska NU-1100 (f) Texas U-40 End A End B A pp lie d lo ad /L o ad at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Deflection under point of application of load/Deflection measured at AASHTO capacity 0 1 2 3 4 5 6 7 End A End B A pp lie d lo ad /L oa d at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Deflection under point of application of load/Deflection measured at AASHTO capacity 0 1 2 3 4 5 6 End A End B A pp lie d lo ad /L o ad at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Deflection under point of application of load/Deflection measured at AASHTO capacity 0 1 2 3 4 5 6 7 8 9 10 End A End B A pp lie d lo ad /L oa d at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Deflection under point of application of load/Deflection measured at AASHTO capacity 0 1 2 3 4 5 6 7 8 9 10 End A End B A pp lie d lo ad /L o ad at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Deflection under point of application of load/Deflection measured at AASHTO capacity 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 End A End B A pp lie d lo ad /L oa d at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Deflection under point of application of load/Deflection measured at AASHTO capacity 0 1 2 3 4 5 Figure 3.7. Normalized load-deflection responses.

64 Strand Debonding for pretensioned Girders Table 3.7. Comparison of normalized peak load and deflection at peak load. Girder Normalized Peak Load Normalized Deflection at Peak Load End A End B End A End B AASHTO BI-36 1.43 (1.84) 1.52 (2.04) 4.58 2.31 AASHTO BT-54 1.51 (1.95) 1.50 (1.92) 3.68 3.37 AASHTO Type III-a 1.69 (2.00) 1.78 (2.05) 5.64 5.47 AASHTO Type III-b 1.63 (1.97) 1.63 (1.92) 4.15 4.62 Nebraska NU-1100 1.21* (1.64) 0.96* (1.21) 1.37 1.00* Texas U-40 1.53 (1.80) 1.00* (1.17) 3.03 1.01* *Not loaded to failure. ( ) capacity ratio based on the nominal material properties, all applicable. AASHTO reductions, and prestressing loss determined per AASHTO LRFD Article 5.9.5.1. Failure mode: Shear compression End A Failure mode: Shear compression End B (a) AASHTO BI-36 Figure 3.8. Failure patterns and modes of failure. 3.5.3.2 Crack Patterns Photo collages of each girder at failure, shown in Figure 3.10, were assembled to determine the angles of diagonal cracks. These collages generally do not indicate any discernible differences between the crack patterns at either end of a given girder. However, for some girders (e.g., Type III-a and Type III-b), End A experienced more cracking and exhibited more of a flexure-shear behavior than End B whose behavior was predominately controlled by web shear. These observations are consistent with the smaller amount of prestressing force (due to greater debonding) at End A.

experimental research approach, Findings, and associated analytical Simulations 65 Failure mode: Shear compression End A Failure mode: Shear compression End B (c) AASHTO Type III-a Failure mode: Shear tension End A Failure mode: “Sliding shear” at the web-flange interface End B (b) AASHTO BT-54 Figure 3.8. (Continued).

Figure 3.8. (Continued). Failure mode: Shear tension and bearing End A (e) Texas U-40 End B was not loaded to failure Failure mode: Shear compression End A Failure mode: Shear compression End B (d) AASHTO Type III-b Figure 3.9. Dowel action evident in AASHTO Type III-b.

experimental research approach, Findings, and associated analytical Simulations 67 Figure 3.10. Photo collages of crack patterns. North face South face Max. dr = 0.60 End A Max. dr = 0.10 End B (b) AASHTO BT-54 North face South face Max. dr = 0.50 End A Max. dr = 0.18 End B (a) AASHTO BI-36 (continued on next page)

68 Strand Debonding for pretensioned Girders North face South face Max. dr = 0.50 End A Max. dr = 0.25 End B (c) AASHTO Type III-a North face South face Max. dr = 0.56 End A Max. dr = 0.22 End B (d) AASHTO Type III-b Figure 3.10. (Continued).

experimental research approach, Findings, and associated analytical Simulations 69 North face South face Max. dr = 0.45 End A Max. dr = 0.27 End B (e) Nebraska NU-1100 North face South face Max. dr = 0.50 End A Max. dr = 0.23 End B (f) Texas U-40 Figure 3.10. (Continued).

70 Strand Debonding for pretensioned Girders As evident from Table 3.8, the average crack angles were essentially the same for the two ends of a single girder having different debonding ratios. The crack widths at End A, which had a larger debonding ratio than End B, were generally slightly wider than those at End B. However, the maximum measured crack widths corresponding to the AASHTO-predicted capacities are small; the largest crack width was less than 0.03 in. The larger dr did not have a deleterious effect on observed crack angles or crack widths. 3.5.3.3 Shear Deformation Using the displacements measured by the diagonal displacement transducers (see Appendix G), the average shear deformations in two adjacent regions were obtained: Region 1 is approximately one-half the shear span closer to the support, and Region 2 is the other half of the shear span closer to the applied load. The relationship between the normalized shear and average shear strains in these regions is shown in Figure 3.11. In this figure, the normalizing “shear at AASHTO capacity” refers to the shear capacity determined using measured material properties, prestress loss inferred from the strains measured by the vibrating wire gages, and taking the resistance factors as unity. The diagonal sensors used to obtain this data were removed prior to reaching the failure load. The load at which the displacement transducers were removed was not always identical for End A and End B in the same girder. In general, the shear strain for a given value of applied shear at End A was larger than that at End B. The smaller amount of prestressing force (resulting from the larger dr) at End A could not restrain the growth and widening of the cracks as well as in End B. 3.5.3.4 Shear Resistance from Transverse Reinforcement The measured stress-strain relationships were used to infer stresses in the transverse rein- forcement. The measured relationships are presented in Appendix F and are modeled in the more appropriate of two ways as indicated in Appendix F. If the measured stress-strain relation- ships exhibited a well-defined yield point, a trilinear stress-strain model, such as that shown in Figure 3.12(a), was used. The values defining the model ( fy, Es, Esh, ey, and esh) were obtained based on the data from material testing (Appendix F). In the absence of a well-defined yield point, a Ramberg-Osgood (R-O) (Ramberg and Osgood 1943) function [Figure 3.12(b) and Eq. 3.5] was calibrated to fit the experimentally obtained stress-strain relationships of the reinforcing steel. This continuous function is more precise than the conventional elastic-perfectly plastic assumptions used in design. 1 1 Eq. 3.51f E A A B fss s C C pu( )= ε + − + ε    ≤ Table 3.8. Average measured angles of diagonal cracks. Girder End A End B Max. dr (deg.) wmax (in.) Max. dr (deg.) wmax (in.) AASHTO BI-36 0.50 29 0.01 0.18 30 0.01 AASHTO BT-54 0.60 34 0.025 0.10 32 0.022 AASHTO Type III-a 0.50 35 0.028 0.25 35 0.014 AASHTO Type III-b 0.56 33 0.015 0.22 34 0.025 Nebraska NU-1100 0.45 32 * 0.27 32 0.015 Texas U-40 0.50 32 0.014 0.23 34 0.01 : Average angle of diagonal cracks measured at the conclusion of testing. wmax: Maximum crack width at a load nearly equal to the AASHTO-predicted girder capacity. *: Not measured.

experimental research approach, Findings, and associated analytical Simulations 71 (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a (d) AASHTO Type III-b (e) Nebraska NU-1100 (f) Texas U-40 End A (Region 1) End A (Region 2) End B (Region 1) End B (Region 2)Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Average shear strain (%) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 End A (Region 1) End A (Region 2) End B (Region 1) End B (Region 2)Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Average shear strain (%) 0 0.05 0.10 0.15 End A (Region 1) End A (Region 2) End B (Region 1) End B (Region 2)Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Average shear strain (%) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 End A (Region 1) End A (Region 2) End B (Region 1) End B (Region 2)Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Average shear strain (%) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 End A (Region 1) End A (Region 2) End B (Region 1) End B (Region 2)Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Average shear strain (%) 0 0.05 0.10 0.15 0.20 End A (Region 1) End A (Region 2) End B (Region 1) End B (Region 2)Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Average shear strain (%) 0 0.05 0.10 0.15 Figure 3.11. Normalized applied shear vs. average shear strain. Where: A, B, and, C = Parameters established from a best fit of experimental stress-strain data. The values of these parameters are summarized in Appendix F. fss = Steel stress fpu = Ultimate strength Es = Modulus of elasticity usually taken as 29,000 ksi e = Strain

72 Strand Debonding for pretensioned Girders For AASHTO BT-54 and Texas U-40, the R-O model in Figure 3.12(b) was used while the stress-strain relationships for the transverse steel in the other girders were characterized based on the elastic-plastic model shown in Figure 3.12(a). The calibrated equation was used to infer stresses corresponding to the strains measured by the strain gages bonded to the transverse reinforcement. Based on Article 5.8.3 in AASHTO LRFD Bridge Design Specifications, the shear resistance provided by the transverse steel, Vs, was computed. AASHTO LRFD Eq. 5.8.3.3-4 was modified slightly by using the experimentally inferred stress ( fv) instead of the yield strength of transverse reinforcement ( fvy), as shown in Eq. 3.6. V A f d s A f d s s v v v v v vcot cot sin cot Eq. 3.6 ( ) ( ) = θ + α α = θ The value of q was selected based on the values tabulated in Table 3.8. This calculation was performed at six locations (1, 2, 3, 4, 5, and 6 ft from the ends of the girder) where the transverse reinforcement had been instrumented. Since there was no inclined prestressing strand, the dif- ference between the applied shear and the average of Vs from these six locations corresponds to the concrete contribution to shear resistance. The resulting concrete contribution to shear capacity as a function of deflection under the load point is plotted in Figure 3.13. For a given value of deflection, the concrete shear resistance at End A (greater dr) is less than its counterpart in End B. This observation is consistent with the differences in the amount of prestressing force at the two ends. The smaller prestressing force at End A resulted in more cracking and hence a reduction in the contribution of the concrete to the shear resistance, as evident from Table 3.9. This reduction at the AASHTO-predicted capacity is not, however, proportional to the relative magnitude of drs at the two ends. For instance, the concrete at End A resisted 15% less shear than End B in AASHTO BT-54, which had the greatest difference between the drs at the two ends, but AASHTO Type III-b exhibited the largest apparent reduction in concrete contribution (19%) even though the difference between the drs at its two ends was less substantial. 3.5.3.5 Apparent Strand Slip Displacement transducers measured the movements of the instrumented strands relative to the end surface of the girder (see Appendix G). For fully bonded strands, this movement is the actual slip. In the case of debonded strands, the strand is assumed to be unstressed between the point of measurement and the beginning of strand embedment (at 3, 6, 9, or 12 ft into the beam); thus, the debonded portion of strand is moving as a rigid body. However, due to flexure- and shear-induced tensile strains, the concrete mass between the end of the girder and the begin- ning of strand embedment is elongating, i.e., ecl in Figure 3.14 where ec = concrete longitudinal Figure 3.12. Modeling of stress-strain relationships for steel reinforcing. (a) Trilinear idealization of stress-strain diagram (b) Ramberg-Osgood idealization of stress- strain diagram Es y sh fy Esh Stress, fss Stress, fss Strain, Es AEs Strain, E(1-A)/B C is a measure of transition "roundness"

Figure 3.13. Concrete shear resistance vs. deflection. (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a (d) AASHTO Type III-b (e) Nebraska NU-1100 (f) Texas U-40 End A End BSh ea r re sis ta n ce fro m co n cr et e (ki ps ) 0 30 60 90 120 150 180 210 240 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 End A End BSh ea r re sis ta n ce fro m co n cr et e (ki ps ) 0 40 80 120 160 200 240 280 320 360 400 Deflection under point of application of load (in.) 0 0.6 1.2 1.8 End A End BSh ea r re sis ta n ce fro m co n cr et e (ki ps ) 0 70 140 210 280 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 End A End BSh ea r re sis ta n ce fro m co n cr et e (ki ps ) 0 50 100 150 200 250 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 End A End BS he ar re sis ta n ce fro m co n cr et e (ki ps ) 0 40 80 120 160 200 240 280 Deflection under point of application of load (in.) 0 0.15 0.30 0.45 0.60 End A End BSh ea r re sis ta nc e fro m co n cr et e (ki ps ) 0 40 80 120 160 200 240 280 320 360 400 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 Table 3.9. Normalized concrete shear resistance at AASHTO-predicted girder capacities. Girder End A End B % Reduction in Max. dr Vc / f'cbvdv Max. dr Vc / f'cbvdv Vc / f'cbvdv AASHTO BI-36 0.50 0.19 0.18 0.20 5% AASHTO BT-54 0.60 0.17 0.10 0.20 15% AASHTO Type III-a 0.50 0.14 0.25 0.16 13% AASHTO Type III-b 0.56 0.13 0.22 0.16 19% Nebraska NU-1100 0.45 0.23 0.22 0.23 0% Texas U-40 0.50 0.24 0.22 0.26 8%

74 Strand Debonding for pretensioned Girders strain and l = the length over which the strand is debonded. The slip measured at the end of the girder on debonded strands will, therefore, be greater than the actual slip exhibited at the beginning of strand embedment (a distance l into the girder). The difference between measured slips and actual slips will, therefore, be proportional to the unbonded length (Hypothesis A). This proportionality is unlikely to be linear since the strains concerned are not uniform over the debonded lengths. The strains causing the concrete deformation can only be assessed in a very general fashion because the available data (the strains measured by the vibrating wire gages every 1 ft up to 5 ft into the girder) did not have sufficient resolution. It was, therefore, not deemed appropriate to attempt to correct measured slip values to account for ec l. The strains will also be affected by the location of the strand in the section (since a strain gradient is present) and by the extent and pattern of local cracking. Nonetheless, in a broad sense it may be hypothesized (Hypothesis B) that the concrete strains will be greater at End A because of the smaller prestressing force in com- parison to End B. The over-estimation of the actual slip at the beginning of strand embedment will, therefore, be greater at End A. The relationships between the normalized applied shear and apparent slip of bonded and debonded strands having various debonding lengths are plotted in Figure 3.15. The values of apparent slip at the AASHTO-predicted capacity are summarized in Table 3.10. Based on the presented data, the following observations about “measured slip” may be drawn: 1. At AASHTO-predicted girder capacities, measured slip rarely exceeded 0.04 in., except for Texas U-40. The measured slip of fully bonded strands was negligible in all cases. 2. In all cases, although the measured slip was negligible, the effect of specimen initial cracking is evident as a change in slope of the normalized shear-apparent slip curves. 3. Prior to initial cracking, the slope of the slip behavior is inversely proportional to the debond- ing length. This observation is consistent with Hypothesis A. 4. In all but AASHTO BT-54, considering End A strands, the measured slip is typically propor- tional to the unbonded length, which is consistent with Hypothesis A. The measured slips of AASHTO BT-54 are not entirely consistent: the strand having 9 ft debonding has the lowest measured slip of the debonded strands. 5. Beyond the AASHTO-predicted capacity, measured slip is observed to increase as cracking and, presumably, yield of strand and embedded steel takes place. 6. Comparing the post-AASHTO capacity of the fully bonded strands, End A is seen to exhibit greater slip at comparable load levels, which supports Hypothesis B. Figure 3.14. Conceptual illustration of elongation of debonded strands.

Figure 3.15. Normalized shear-apparent slip relationships. (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a (d) AASHTO Type III-b (e) Nebraska NU-1100 (f) Texas U-40 End A (bonded) End A (debonded 3') End A (debonded 6') End A (debonded 9') End A (debonded 12') End B (bonded) End B (debonded 3') End B (debonded 6')Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Apparent slip (in.) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 End A (bonded) End A (debonded 3') End A (debonded 6') End A (debonded 9') End B (bonded) End B (debonded 3')A pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Apparent slip (in.) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 End A (bonded) End A (debonded 3') End A (debonded 6') End A (debonded 9') End B (bonded) End B (debonded 3') End B (debonded 6')Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Apparent slip (in.) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 End A (bonded) End A (debonded 3') End A (debonded 6') End A (debonded 9') End B (bonded) End B (debonded 3') End B (debonded 6')Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Apparent slip (in.) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 End A (bonded) End A (debonded 3') End A (debonded 6') End A (debonded 9') End A (debonded 12') End B (bonded) End B (debonded 3') End B (debonded 12')Ap pl ie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Apparent slip (in.) 0 0.025 0.050 0.075 0.100 End A (bonded) End A (debonded 3') End A (debonded 6') End A (debonded 9') End B (bonded) End B (debonded 3') End B (debonded 6') End B (debonded 9')A pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Apparent slip (in.) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 Girder Bonded Strands Debonded Strands ldebond = 3 ft ldebond = 6 ft ldebond = 9 ft ldebond = 12 ft End A End B End A End B End A End B End A End B End A End B AASHTO BI-36 < 0.001 < 0.001 0.016 0.004 0.019 < 0.001 0.016 N/A 0.002 N/A AASHTO BT-54 0.009 0.004 0.041 0.008 0.043 N/A 0.023 N/A N/A N/A AASHTO Type III-a 0.004 < 0.001 0.005 0.002 0.011 0.006 0.010 N/A N/A N/A AASHTO Type III-b < 0.001 < 0.001 0.008 < 0.001 0.018 0.006 0.022 N/A N/A N/A Nebraska NU-1100 0.005 0.002 0.033 0.011 0.035 N/A 0.039 N/A 0.040 0.030 Texas U-40 0.011 0.003 0.036 0.060 0.073 0.034 0.103 0.099 N/A N/A Table 3.10. Apparent strand slip at AASHTO-predicted capacity.

76 Strand Debonding for pretensioned Girders 7. Comparing the measured slip of the End A and End B strands having unbonded lengths of 3 ft (the only strands available for such comparison), End A, having greater debonding, exhibits greater slip except for Texas U-40. This observation supports Hypothesis B. Thus, both Hypotheses A and B are supported by experimental observations: (A) the difference between measured slips and actual slips is proportional to the unbonded length; and (B) the con- crete strains will be greater at End A because of the smaller prestressing force in comparison to End B. 3.5.3.6 Contribution of Longitudinal Reinforcement The amount of required nonprestressed longitudinal reinforcement at the critical section and at the interior face of the support had been determined according to AASHTO LRFD Eq. 5.8.3.5-1 and Eq. 5.8.3.5-2., respectively: 0.5 0.5 cot 5.8.3.5–1A f A f M d N V V Vps ps s y u v f u c u v p s [ ]+ ≥ φ + φ + φ − −     θ 0.5 cot 5.8.3.5–2A f A f V V Vps ps s y u v s p [ ]+ ≥ + φ − −     θ Based on a similar procedure discussed in Section 3.5.3.4, stresses in the nonprestressed lon- gitudinal reinforcement were inferred from the measured strains. The R-O function given by Eq. 3.5 and shown in Figure 3.12b was used for all the girders except for AASHTO BI-36 and Texas U-40 girder, for which the nonprestressed longitudinal reinforcement stress-strain relationships were based on the trilinear function depicted in Figure 3.12a. The resulting stresses normalized with respect to the nonprestressed reinforcement yield strength are plotted in Figure 3.16 against the normalized applied shear. If available, stresses at three sections are plotted: (1) at the critical section near the support, (2) dv from the interior face of the support, and (3) at the point where the load was applied. The following observations are made: 1. At AASHTO-predicted capacity (i.e., when the normalized shear is unity), the stress in the nonprestressed reinforcing steel is at most 0.56fy, as can be seen more clearly from Table 3.11. However, the longitudinal nonprestressed reinforcement is assumed to have yielded accord- ing to AASHTO LRFD Eq. 5.8.3.5-1 and Eq. 5.8.3.5-2. A plausible explanation for this dif- ference could be that AASHTO LRFD Bridge Design Specifications do not account for the tensile strength of the precompressed concrete. Hence, the available capacity (in the absence of nonprestressed reinforcement) is larger than Aps fps alone. 2. For the girders that were loaded to failure, the nonprestressed longitudinal bars had begun to yield at sections 2 and 3, i.e., at the critical section near the support and dv from the interior face of the support, respectively. 3.6 Summary The experimentally determined girder capacities exceed those computed based on AASHTO LRFD Bridge Design Specifications using the measured material properties and prestress losses with no strength reduction factor. Regardless of the drs, the measured deflection at the peak load was several times larger than the measured deflection at the calculated AASHTO capacity. The nonprestressed reinforcement used to compensate for larger prestressed reinforcing drs is adequate in terms of capacity. Even though this reinforcement cannot replicate the effects of prestressing force in bonded strands, the differences in the overall stiffness, crack widths, and

(a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a (d) AASHTO Type III-b (e) Nebraska NU-1100 (f) Texas U-40 End A (Section 2) End A (Section 3) End A (Section 4) Section 2: critical section near support Section 3: dv from the face of support Section 4: at application of load End B did not have nonprestressed reinforcementA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Stress in nonprestressed reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 End A (Section 2) End A (Section 3) End A (Section 4) End B (Section 2) End B (Section 3) Section 2: critical section near support Section 3: dv from the face of support Section 4: at application of load Nonprestressed reinforcement at End B was terminated prior to Section 4.A pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Stress in nonprestressed reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 End A (Section 2) End A (Section 3) End A (Section 4) End B (Section 2) End B (Section 3) End B (Section 4) Section 2: critical section near support Section 3: dv from the face of support Section 4: at application of loadA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Stress in nonprestressed reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 End A (Section 2) End A (Section 3) End A (Section 4) End B (Section 2) End B (Section 3) End B (Section 4) Section 2: critical section near support Section 3: dv from the face of support Section 4: at application of loadA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Stress in nonprestressed reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 End A (Section 2) End A (Section 3) End B (Section 2) End B (Section 3) Section 2: critical section near support Section 3: dv from the face of supportA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Stress in nonprestressed reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 End A (Section 2) End A (Section 3) End B (Section 2) End B (Section 3) Section 2: critical section near support Section 3: dv from the face of support Section 4: at application of load Strain gages at Section 4 malfunctioned. A pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Stress in nonprestressed reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Figure 3.16. Normalized stress in nonprestressed longitudinal reinforcement. Girder End A End B Max. dr fs /fy Max. dr fs /fy Section 2 Section 3 Section 4 Section 2 Section 3 Section 4 AASHTO BI-36 0.50 0.03 0.11 0.21 0.18 N/A AASHTO BT-54 0.60 0.12 0.23 0.15 0.10 0.17 0.20 N/A AASHTO Type III-a 0.50 0.12 0.14 0.15 0.25 0.04 0.11 0.16 AASHTO Type III-b 0.56 0.07 0.23 0.27 0.22 0.20 0.08 0.03 Nebraska NU-1100 0.45 0.56 0.10 N/A 0.27 0.31 0.09 N/A Texas U-40 0.50 0.35 0.28 N/A 0.23 0.30 0.18 N/A Table 3.11. Normalized stress in nonprestressed longitudinal reinforcement at AASHTO-predicted girder capacities.

78 Strand Debonding for pretensioned Girders crack patterns and angle of cracks of the two girder ends, with different magnitudes of drs, were found to be small. The results are consistent with the hypothesis that bonded strand and nonprestressed tension reinforcement work together to resist longitudinal forces induced by shear (i.e., those calculated using AASHTO LRFD Eq. 5.8.3.5-1 and -2 provided the detailing rules shown in Table 3.2 and elaborated upon in Section 4.2 are satisfied). 3.7 Modeling of Test Specimens The FEM platform described in Section 2.4 and STM modeling described in Section 2.5 were applied to the test girders in order to both validate the analytical approaches and to gain a better understand of observed experimental behavior. 3.7.1 FEM Simulation of Test Girders Reinforcing steel and concrete material properties were selected based on those determined experimentally for each girder. Due to the test times, concrete properties vary from End A to End B; this variation was captured in the models. The material properties used to model each girder are summarized in Table 3.12. The transfer length was taken as 30db, which is consid- ered to be more realistic of in situ behavior than 60db used in AASHTO LRFD Bridge Design Specifications. As evident from Figure 3.17, the load-deflection responses determined from FEM predict the experimental curves quite well. The “saw tooth” behavior of the experimental curves reflects the relaxation of the applied load when loading was paused to inspect the girders for cracking and checking the data. The observed and predicted crack patterns at failure are compared in Figure 3.18. The crack patterns based on nonlinear FEM analysis replicate those observed rea- sonably well. 3.7.2 Utilization of Calibrated Analytical FEM Platform As evident from the results shown in Section 3.7.1, the overall measured responses of the test girders are quite close to those predicted by the FEM platform. Using the platform, additional analyses were conducted to (1) further evaluate the transfer lengths and (2) examine the ramifi- cations of rebonding a large number of previously debonded strands. 3.7.2.1 Transfer Length The distribution of the longitudinal strain at prestress force transfer (release) was computed by FEM analysis. As shown in Figure 3.19, the FEM results are generally close to those deter- mined using fundamental mechanics (see Section 3.4). The results for Texas U-40 girder are dis- cussed in Section 3.7.2.2. At a few locations, the strains from FEM are closer to the measured data in comparison to those from basic principles. Nevertheless, a number of the measured strains do not correspond to those based on FEM analysis. The field boundary conditions include some restraint from the forms and are therefore different from a simple span that is used in the cal- culations and analyses. 3.7.2.2 Further Evaluation of Longitudinal Strains at Release in Texas U-40 In the Texas U-40 girder, the concrete strains measured at release were markedly smaller than those determined from fundamental mechanics, AASHTO, or NCHRP Report 603 methods, all

experimental research approach, Findings, and associated analytical Simulations 79 Table 3.12. FEM material properties. Girder concrete f’c ksi BI-36 BT-54 NU-1100 End A End B End A End B End A End B 12.6 12.2 17.4 15.2 14.0 13.2 Ec ksi 6472 6434 7592 7096 6550 6513 ft psi 760 740 870 820 810 780 0.20 Slab concrete f’c ksi N/A N/A 11.4 11.2 6.9 6.1 Prestressing strand fpu ksi 270 fpi ksi 0.75fpu = 202.5 No. 3 transverse steel fy ksi N/A 65 75 fu ksi 97 101 u 0.200 0.238 No. 4 transverse steel fy ksi 68 70 79 fu ksi 103 107 106 u 0.114 0.127 0.250 No. 5 longitudinal steel fy ksi N/A N/A 70 fu ksi 103 u 0.128 No. 6 longitudinal steel fy ksi 69 66 69 fu ksi 108 106 109 u 0.144 0.132 0.120 Girder concrete f’c ksi Type III-a Type III-b Texas U-40 End A End B End A End B End A End B 12.6 12.2 13.8 13.2 12.8 12.0 Ec ksi 6473 6454 6542 6513 6511 6304 ft psi 760 750 806 780 750 730 0.20 Slab concrete f’c ksi 7.4 6.2 6.2 5.7 5.9 5.8 Prestressing strand fpu ksi 270 fpi ksi 0.75fpu = 202.5 No. 3 transverse steel fy ksi 75 N/A fu ksi 111 u 0.258 No. 4 transverse steel fy ksi 64 71 fu ksi 100 110 u 0.223 0.157 No. 5 longitudinal steel fy ksi 76 67 fu ksi 113 106 u 0.232 0.093 No. 6 longitudinal steel fy ksi N/A 68 fu ksi 110 u 0.145 using a plane sections assumption. The experimental strains were measured along the centerline of the girder at approximately the mid-depth of the bottom flange corresponding to approxi- mately location 1 shown in Figure 3.20. As seen in Figure 3.20, the strand layout was concentrated toward the webs of the girder. Due to the flexibility of the open section, the webs are expected to resist most of the flexural strains/ stresses at release. Furthermore, the axial strains are developed over the transfer length and are distributed into the concrete as a diagonal strut, rather than engaging the entire cross section immediately. Taken together, it may be expected that the strains in the flange would be notably reduced over a much longer length of the girder. This hypothesis was tested using the calibrated FEM model for the test specimen (see Section 3.7.1). Figure 3.21 shows a view of the longitudinal strains in the girder soffit confirming the hypothesis. There is a distinct shear lag effect along the girder flange. Figure 3.22 shows the measured and FEM-predicted strains along the girder following pre- stress transfer. The results from basic principles are also provided. The FEM-predicted strains

80 Strand Debonding for pretensioned Girders Figure 3.17. Measured vs. FEM-computed load-deflection relationships. (a) AASHTO BI-36 (c) AASHTO Type III-a End A End B Experimental FEM A pp lie d lo ad (ki ps ) 0 50 100 150 200 250 300 350 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 3.0 Experimental FEM A pp lie d lo ad (ki ps ) 0 50 100 150 200 250 300 350 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 3.0 End A End B Experimental FEM A pp lie d lo ad (ki ps ) 0 100 200 300 400 500 600 700 800 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 Experimental FEM A pp lie d lo ad (ki ps ) 0 100 200 300 400 500 600 700 800 0 Deflection under point of application of load (in.) 0.5 1.0 1.5 2.0 (b) AASHTO BT-54 End A End B Experimental FEM A pp lie d lo ad (ki ps ) 0 50 100 150 200 250 300 350 400 450 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 3.0 Experimental FEM A pp lie d lo ad (ki ps ) 0 50 100 150 200 250 300 350 400 450 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 3.0

experimental research approach, Findings, and associated analytical Simulations 81 (d) AASHTO Type III-b (e) Nebraska NU-1100 End A End B End A End B End A End B (f) Texas U-40 Experimental FEM A pp lie d lo ad (ki ps ) 0 100 200 300 400 500 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 3.0 Experimental FEM A pp lie d lo ad (ki ps ) 0 100 200 300 400 500 Deflection under point of application of load (in.) 0 0.5 1.0 1.5 2.0 2.5 3.0 Experimental FEM A pp lie d lo ad (ki ps ) 0 100 200 300 400 500 Deflection under point of application of load (in.) 0 0.1 0.2 0.3 0.4 0.5 0.6 Experimental FEM A pp lie d lo ad (ki ps ) 0 100 200 300 400 500 Deflection under point of application of load (in.) 0 0.1 0.2 0.3 0.4 0.5 0.6 Experimental FEM A pp lie d lo ad (ki ps ) 0 200 400 600 800 1000 Deflection under point of application of load (in.) 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Experimental FEM A pp lie d lo ad (ki ps ) 0 200 400 600 800 1000 Deflection under point of application of load (in.) 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Figure 3.17. (Continued).

82 Strand Debonding for pretensioned Girders (a) AASHTO BI-36 (b) AASHTO BT-54 Test specimen at failure Peak load FEM: 318 kips, Test: 297 kips FEM: 341 kips, Test: 336 kips All predicted cracks Cracks > 0.004 in. Cracks > 0.008 in. End A End B Test specimen at failure Peak load FEM: 630 kips, Test: 640 kips FEM: 720 kips, Test: 724 kips All predicted cracks Cracks > 0.004 in. Cracks > 0.008 in. End A End B Test specimen at failure Peak load FEM: 379 kips, Test: 388 kips FEM: 421 kips, Test: 446 kips All predicted cracks Cracks > 0.004 in. Cracks > 0.008 in. End A End B (c) AASHTO Type III-a Figure 3.18. Observed and FEM-predicted crack patterns.

experimental research approach, Findings, and associated analytical Simulations 83 (d) AASHTO Type III-b (e) Nebraska NU-1100 Test specimen at failure Peak load FEM: 395 kips, Test: 401 kips FEM: 440 kips, Test: 478 kips All predicted cracks Cracks > 0.004 in. Cracks > 0.008 in. End A End B Test specimen at failure Peak load FEM: 470 kips, Test: 468 kips FEM: 350 kips, Test: 346 kips All predicted cracks Cracks > 0.004 in. Cracks > 0.008 in. End A End B Test specimen at failure Peak load FEM: 890 kips, Test: 998 kips FEM: 693 kips, Test: 710 kips All predicted cracks Cracks > 0.004 in. Cracks > 0.008 in. End A End B (f) Texas U-40 Figure 3.18. (Continued).

84 Strand Debonding for pretensioned Girders Figure 3.19. Comparison of measured and computed longitudinal strains at release. (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a

experimental research approach, Findings, and associated analytical Simulations 85 Figure 3.19. (Continued). (d) AASHTO Type III-b (e) Nebraska NU-1100 (a) End A (b) End B Figure 3.20. Cross section of U-40 test girder. Figure 3.21. Longitudinal strains along girder soffit (reverse plan view). End B End A - 0. 00 04 0 - 0. 00 03 8 - 0. 00 03 6 - 0. 00 03 4 - 0. 00 03 2 - 0. 00 03 0 - 0. 00 02 8 - 0. 00 02 6 - 0. 00 02 4 - 0. 00 02 2 - 0. 00 02 0 - 0. 00 01 8 - 0. 00 01 6 - 0. 00 01 4 - 0. 00 01 2 - 0. 00 01 0 - 0. 00 00 8 - 0. 00 00 6 - 0. 00 00 4 - 0. 00 00 2 0. 00 00 0 0. 00 00 2 0. 00 00 4 0. 00 00 6 0. 00 00 8 0. 00 01 0

86 Strand Debonding for pretensioned Girders are shown along the girder centerline (strand location 1 shown in Figure 3.20) and near the web at strand location 14 (Figure 3.20) at increments of 23.6 in. along the girder length. The FEM predictions capture the markedly reduced strains observed along the girder centerline, confirm- ing the research team’s hypothesis. 3.7.2.3 STM Simulation of Test Girders Each test girder had a single instrumented transverse tie at each end (see Appendix G). Using the measured strains, the stresses were inferred using a procedure similar to that described in Section 3.5.3.4. In Figure 3.23, the inferred stress normalized with respect to fy is plotted against the normalized applied shear. The STM was applied to both the design and as-built experimental behavior of the single-web test beams. The model parameters and results are given in Table 3.13. As is seen, the ties provided in the as-built beams exceeded the requirements determined from the STM. Additionally, when experimentally determined tie yield stress values are used, the capacity of the as-built tie details met or exceeded the predicted tie capacity demand at the ultimate observed shear (Vexp). Using the calculated tie force corresponding to Vexp (Table 3.13), the stress in each confin- ing reinforcement bar was obtained by assuming a uniform stress for all confining bars within Figure 3.22. Measured strains vs. computed values in Texas U-40.

experimental research approach, Findings, and associated analytical Simulations 87 Figure 3.23. Stress in confinement reinforcement. (a) AASHTO BI-36 (b) AASHTO BT-54 (c) AASHTO Type III-a (d) AASHTO Type III-b (e) Nebraska NU-1100 (f) Texas U-40 End A End BA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Stress in confinement reinforcement/fy 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 End A End BA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Stress in confinement reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 End A End BA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Stress in confinement reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 End A End B A pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Stress in confinement reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 End A End BA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Stress in confinement reinforcement/fy 0 0.1 0.2 0.3 0.4 End A End BA pp lie d sh ea r/S he ar at A A SH TO ca pa ci ty 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Stress in confinement reinforcement/fy 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

88 Strand Debonding for pretensioned Girders H/4 + Lbearing. Figure 3.24 illustrates the relationship between the resulting stress (normalized with respect to the yield strength) and the experimentally inferred stress. The correlation between the computed and experimental data is excellent considering the complexity of assessing behavior of confining reinforcement. All specimens appear to have experienced some degree of transverse cracking, and the transverse steel, which remained elastic in all cases, controlled such cracking. The nature of the tension tie-induced longitudinal cracking is such that it is expected to propagate from the dr BT-54 NU-1100 Type III-a Type III-b End A End B End A End B End A End B End A End B 0.60 0.11 0.45 0.38 0.50 0.30 0.56 0.29 H (in.) 60 60 49 49 51 51 51 51 N 8 18 12 16 8 12 8 14 nf 3 7 5 6 2 2 2 3 xp (in.) 7.7 6.1 9.8 9.7 8.0 8.0 8.0 7.0 yp (in.) 2.7 3.1 2.4 2.3 3.0 3.0 3.0 3.3 hb (in.) 10.5 10.5 12.7 12.7 14.5 14.5 14.5 14.5 bb (in.) 22 22 36.8 36.8 20 20 20 20 cb (in.) 6.9 6.7 10.7 11.5 7.5 8.3 7.5 7.9 0.478 0.253 0.233 0.054 0.216 0.097 0.216 0.079 Vdes, (kips) 300 341 311 277 184 201 198 236 t = Vdesign (kips) 143 86 72 15 40 20 43 19 Ties req’d (No. @ in.)1 7 @ 4.5 4 @ 9 4 @ 8 1 2 @ 25 1 2 @ 25 1 Vexp. (kips) 452 511 375 277 311 357 321 383 t = Vexp (kips) 216 129 87 15 67 35 69 30 fy of ties (ksi) 70 70 79 79 64 64 64 64 Ties req’d (No. @ in.)1 9 @ 3.4 6 @ 5.4 4 @ 8 1 3 @ 12.5 2 @ 25 4 @ 8.3 2 @ 25 Ties provided1 9 @ 3 4 @ 3 + 2 @ 6 4 @ 3 + 2 @ 6 4 @ 3 + 2 @ 6 Tie stress Figure Figure 3.23b Figure 3.23e Figure 3.23c Figure 3.23d Initial transverse cracking 0.7Vdes 0.85Vdes 0.3Vdes 0.4Vdes 0.5Vdes 1.0Vdes 0.95Vdes 1.1Vdes Maximum tie stress 0.84fy 0.73fy 0.37fy 0.22fy 0.45fy 0.20fy 0.63fy 0.26fy 1No. 4 hoops located over a distance H/4 + Lbearing; Lbearing = 12 in. in all cases Table 3.13. STM of test specimen bulb confinement. NU-1100 (End B) Type IIIa (End B) Type IIIb (End B) NU-1100 (End A) Type IIIa (End A) Type IIIa (End A) BT-54 (End B) BT-54 (End A) Best linear fit (R2 = 0.83) M ax im u m m ea su re d tie fo rc e (1/ f y) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Predicted tie force (1/fy) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 3.24. Predicted vs. inferred tie stress.

experimental research approach, Findings, and associated analytical Simulations 89 bearing. An example is shown in Figure 3.25 showing the 36.8 in. wide soffit of NU-1100 End A. Each transverse line is a distance of approximately H/4 (the lines are spaced at 12 in. while H/4 = 12.25 in.). The cracks resulting from loading clearly propagate from the bearing and extend as far as H/2 from the face of the bearing. 3.8 Web Cracking Web cracking has long been a concern for thin-webbed prestressed concrete girders. The AASHTO Standard Specifications for Highway Bridges (1997) required that the factored shear force be checked against the term Vcw. Vcw was defined as the shear force at the section required to create a maximum principal tensile stress of 0.125√f ′c in ksi units in the web at the neutral axis of the section resisting external loads (i.e., the composite section neutral axis for composite beams, and the non-composite neutral axis for non-composite beams). If the neutral axis fell within the top flange, the stress was calculated at the web/top flange interface. In lieu of calculating the principal stress, a simplified equation could be used. It was known that limiting the total shear force to 0.125√f ′c (ksi), which was the assumed stress required to crack the web, was conservative, but it was considered the best approach available at the time. The first edition of the AASHTO LRFD Bridge Design Specifications did not include Vcw or the companion Vci flexural shear strength checks. The sectional method (a.k.a. the modified compression field theory) in the AASHTO LRFD Bridge Design Specifications was adequate to address web-cracking issues. However, the original version of the sectional method was difficult to use and to automate in a computer code, as it required the use of tables and iteration. In 2007, AASHTO restored Vcw and Vci checks to the LRFD Bridge Design Specifications as the simplified method (Article 5.8.3.4.3). The only change from the form used in the Standard Specifications was the crack angle, q, had to be calculated when Vcw was less than Vci (the crack angle was assumed as 45° for Vci and was assumed as 45° for Vcw in the Standard Specifications). Concerns over web cracking remain. Web cracking is addressed in two articles of the cur- rent AASHTO LRFD Articles 5.8.3.4.3 and 5.8.5. Article 5.8.3.4.3 is the simplified method of determining shear resistance of concrete sections. Vcw controls near the end of the girder where debonding, if present, occurs. Hence, it is necessary to determine whether debonding has any influence on this calculation. In June 2016, the AASHTO Subcommittee on Bridges and Struc- tures (SCOBS) approved a reorganization of Section 5 of the AASHTO LRFD Bridge Design Spec- ifications for publication in 2017. As part of this reorganization, the simplified method utilizing Figure 3.25. Soffit of NU-1100 End A following testing.

90 Strand Debonding for pretensioned Girders Vcw and Vci was eliminated. Consequently, the need to determine whether debonding has any influence on the calculation of Vcw will no longer exist. However, this effect was investigated as part of this project before it was known that the article would be deleted. AASHTO LRFD Article 5.8.5 requires that the principal tensile stress in the web of segmen- tal box girders be investigated. The principal tensile stress may not exceed 0.11√ f ′c ksi under Service III loading. As part of the reorganization of Section 5, this article was extended to apply to all prestressed concrete sections with compressive strengths used for design greater than 10 ksi. In anticipation of this implementation in 2017, the effect of debonding on web principal tensile stresses was investigated. AASHTO LRFD Articles 5.8.3.4.3 and 5.8.5 were examined using the experimental data obtained as part of this project and previous studies reported in Shahawy et al. (1993 and 1996). 3.8.1 Calculation of Principal Tensile Stress The state of stress in the web is shown in Figure 3.26. The normal stress, fpc, is calculated from Eq. 3.7. f P A P e I y y M y y I M y y I pc pe nc pe nc bnc dnc bnc nc L bc c Eq. 3.7( ) ( ) ( )= − − + − + − In Eq. 3.7, compressive stresses are positive and tensile stresses are negative. The sign of each term provides the correct sense of the stress. The shear stress, v, is calculated from Eq. 3.8. (Also see Figure 3.27.) v V Q t I V Q t I dnc nc w nc L c w c Eq. 3.8= + The principal tensile web stress is then calculated from Eq. 3.9. 2 2 Eq. 3.9 2 2f f f vt pc pc − = −     + Note that the principal stress is shown as negative, indicating tension. 3.8.2 AASHTO LRFD Specifications Article 5.8.5 The following procedure was used to check the web stress in the test girders: 1. The stress was checked at the critical section, dv, from the face of the bearing pad. For simplic- ity, dv was taken as 0.9de where de is the effective depth of the beam. 2. Ppe was calculated at the critical section. The area of the prestressing steel was adjusted to account for debonded strands. Prestress losses were estimated using strain measurements from the girders. In general, this loss was between 3% and 10%. If a debonded strand was bonded before the critical section, the assumed stress in the strand was linearly interpolated if the bonded length was less than the transfer length of 60db. 3. Vdnc and Mdnc were calculated assuming a concrete unit weight of 0.150 kcf. The dead load shears and moments were small compared to the applied load; hence, variation of this assumption would not introduce appreciable error. Figure 3.26. State of web stresses. v v v v fpcfpc

experimental research approach, Findings, and associated analytical Simulations 91 4. VL and ML were calculated from the applied load at the time the first diagonal crack was visu- ally observed in the experiment. 5. Composite section properties were calculated by transforming the deck into an equivalent width of beam concrete using the modulus of elasticity computed based on concrete strength of both the beam and slab concrete measured at the time of testing; otherwise, gross section properties were used. 6. Using Eqs. 3.7, 3.8, and 3.9, the principal tensile stress was calculated at 3 points: (1) the inter- face of the bottom flange and the web, (2) the interface of the top flange and the web, and (3) the composite section neutral axis (for the non-composite BI-36, the non-composite neutral axis was used). The maximum principal tensile stress was compared to the allowable stress of 0.11√f ′c where f ′c is the measured beam concrete strength at the time of testing in ksi. Table 3.14 shows the maximum principal tensile stresses at the occurrence of web crack- ing, calculated at the three locations described in step 6. The stress at the bottom flange/web junction did not control for any of the cases shown. When the maximum principal tensile web stress is compared to the allowable value of 0.11√f ′c, the ratio exceeds 1 for all but the BI-36 box girder. That is, the calculated principal tensile stress at cracking in the web was greater than the minimum allowable stress for all but the box girder. This trend should be expected. The data Figure 3.27. Definition of Q for the area above y for the section shown. Table 3.14. Maximum principal tensile stresses for test girders (f ′c > 10 ksi). Girder End Max. dr f’c (ksi) Maximum Principal Tensile Stresses Allowable Stress 0.11 f’c (ksi) Max Stress Allowable NA Stress Allowable @ Neutral Axis (ksi) @ Web/Top Flange (ksi) @ Web/Bottom Flange (ksi) AASHTO BI-36 A 0.50 12.4 0.323 0.265 0.245 0.387 0.832 0.832 AASHTO BI-36 B 0.18 12.4 0.246 0.231 0.158 0.387 0.634 0.634 AASHTO BT- 54 A 0.60 15.0 0.564 0.616 0.304 0.428 1.44 1.32 AASHTO BT- 54 B 0.10 17.4 0.618 0.804 0.249 0.459 1.75 1.35 AASHTO Type III-a A 0.50 12.4 0.472 0.367 0.460 0.388 1.22 1.22 AASHTO Type III-a B 0.25 12.4 0.407 0.423 0.220 0.388 1.09 1.05 AASHTO Type III-b A 0.56 13.5 0.414 0.362 0.379 0.404 1.02 1.02 AASHTO Type III-b B 0.22 12.5 0.491 0.440 0.440 0.404 1.21 1.21 Nebraska NU-1100 A 0.45 13.6 0.484 0.551 0.399 0.406 1.36 1.19 Nebraska NU-1100 B 0.27 13.6 0.518 0.616 0.406 0.406 1.52 1.28 Texas U-40 A 0.50 12.0 0.506 0.473 0.303 0.381 1.33 1.33 Texas U 40 B 0.23 12.0 0.583 0.586 0.220 0.381 1.54 1.53 Controlling stress is in bold.

92 Strand Debonding for pretensioned Girders for the BI-36 appear to be an anomaly and will be discussed later. Assuming the anomaly of the BI-36 can be explained, the data would indicate that the proposed changes to Article 5.8.5 requiring the principal tensile stress be checked in the webs of all prestressed girders with design strengths above 10 ksi would remain appropriate even for heavily debonded girders such as those described here. Table 3.14 also shows that checking the stress only at the neutral axis is sufficient for all but the box girders. All of the girders in this experimental program had measured concrete strengths exceed- ing 10 ksi. Data reported in Shahawy et al. (1993 and 1996) were used to examine the proposed changes to the AASHTO LRFD Specifications Article 5.8.5 for cases with concrete strengths less than 10 ksi. Using information found in the references, the principal tensile stress check was conducted for the girders with debonded strands where cracking data was available. Based on the previous observations, the maximum principal tensile stress was computed only at the neutral axis of composite section. The cracking load was taken from diagrams provided in the Shahawy et al. 1993 reference. The only concrete strength reported was an average strength of 7 ksi (Shahawy et al. 1996). This value was used for both the girders and the slabs. Table 3.15 shows the results of this analysis. All of the girders reported by Shahawy et al. meet the provision of the calculated principal stress at first cracking exceeding 0.11√f ′c. The smallest ratio is 1.48 and several exceed 2.0. Hence, the proposed provision of Article 5.8.5, which does not require a principal tensile stress check for pretensioned girders with concrete strengths below 10 ksi, appears to be acceptable. 3.8.3 AASHTO LRFD Specifications Article 5.8.3.4.3 The proposed revision to Article 5.8.5 will require a stress check all along the height of the web since the maximum principal tensile stress may not occur at the neutral axis. The data shown in Table 3.14, except that for the BI-36 girder, suggest that checking the stress at the neutral axis is sufficient to prevent web cracking for girders with debonded strands. The value of the stirrup contribution, Vs, to shear capacity depends on the angle of the crack intersecting the stirrups. Based on a Mohr’s Circle analysis, the angle of the crack, q, can be calculated as (Eq. 3.10): 0.5arctan 2 Eq. 3.10 v fpc θ =    Specimen I.D. Max. dr Ratio of Calculated Principal Tensile Stress at NA of Composite Section to 0.11 f’c A2-25-3R N 0.25 2.11 A2-25-3R S 0.25 1.85 A2-50-3R N 0.50 1.78 A2-50-3R S 0.50 1.73 C0-50-R N 0.50 2.42 C0-50-R S 0.50 1.48 C1-25-R N 0.25 1.59 C1-25-R S 0.25 1.52 C1-50-R N 0.50 1.72 C1-50-R S 0.50 1.48 Table 3.15. Maximum principal tensile stresses for Shahawy et al. girders (f ′c < 10 ksi).

experimental research approach, Findings, and associated analytical Simulations 93 In the current version of the AASHTO LRFD Specifications, the crack angle used for deter- mining Vs in conjunction with Vcw is calculated from Eq. 5.8.3.4.3-4 (Eq. 3.11). cot 1.0 3 1.8 Eq. 3.11 f f pc c θ = + ′     ≤ In Table 3.16, the angle calculated from Mohr’s Circle (Eq. 3.10) and that from AASHTO LRFD Eq. 5.8.3.4.3-4 (Eq. 3.11) are compared to the average measured crack angle. All calcu- lations were performed at the neutral axis as the AASHTO equation was developed for crack angles at the neutral axis, and the experimental crack angles were measured at the neutral axis. The angle predicted by the LRFD equations agrees quite well with the angle predicted by Mohr’s Circle, and both agree reasonably well with the measured angles. One important observation is that the measured angles on the “A” ends do not agree as well with the predictions as the “B” ends; the angles on the “A” ends tend to be shallower than predicted. The “A” ends all have the higher drs. In both the Mohr’s Circle and the AASHTO equations, increasing fpc results in a shallower angle. A possible conclusion from the experimental data is that the crack angle on End A is shal- lower due to a higher fpc, and the higher fpc may be caused by the prestressing force being higher than calculated. The higher stress is likely caused by the fact that the calculation assumes that stress in debonded strands after they are rebonded is linear over the transfer length of 60db. In reality, the stress is not linear and the transfer length is likely less than 60db. Thus, the prestress- ing force at the section is likely higher than assumed; this difference would be more pronounced at End A having large drs. When using the simplified method for design, the maximum factored shear force must be less than Vcw in the areas where Vcw controls. Thus, Vcw + Vs should be compared to the total shear force at failure. However, Vcw is defined as the shear force that causes the principal tensile stress to exceed 0.125√f ′c (ksi), which is assumed to crack the web. Thus, it may be appropri- ate also to compare Vcw to the load that causes cracking in the web. Table 3.17 presents both comparisons. Note that the data from Shahawy et al. (1993, 1996) are not included in this table because Vcw had been checked using the Standard Specifications that tend to produce results that are more conservative than those obtained based on AASHTO LRFD Bridge Design Specifications. Girder End Max. dr Measured Angle (deg.) Mohr's Circle (deg.) Eq. 3.10 AASHTO LRFD (deg.) Eq. 3.11 Measured Mohr's Circle Measured AASHTO AASHTO BI-36 A 0.50 28.8 31.3 34.2 0.92 0.84 AASHTO BI-36 B 0.18 29.7 24.8 29.5 1.20 1.01 AASHTO BT-54 A 0.60 33.9 37.5 37.9 0.90 0.89 AASHTO BT-54 B 0.10 31.5 34.3 32.9 0.92 0.96 AASHTO Type III-a A 0.50 34.7 34.7 35.9 1.00 0.97 AASHTO Type III-a B 0.25 34.9 34.3 34.0 1.02 1.03 AASHTO Type III-b A 0.56 32.6 35.5 36.0 0.92 0.90 AASHTO Type III-b B 0.22 33.6 31.3 32.8 1.07 1.02 Nebraska NU-1100 A 0.46 32.3 32.9 32.9 0.98 0.98 Nebraska NU-1100 B 0.27 31.8 31.9 31.0 1.00 1.03 Texas U-40 A 0.50 32.0 38.4 38.5 0.83 0.83 Texas U-40 B 0.23 34.0 37.4 36.7 0.91 0.94 Table 3.16. Crack angles for test girders.

94 Strand Debonding for pretensioned Girders The data shown in Table 3.17 indicate that, for all but the BI-36 girder, the total applied shear force at cracking exceeds Vcw, and the total shear force at failure exceeds Vcw + Vs in all cases except End B in NU-1100; however, this girder end was not loaded to failure. The results shown in Tables 3.16 and 3.17 indicate that no change would be needed to Arti- cle 5.8.3.4.3. Vcw is a conservative prediction of the shear force at failure for all girders tested to failure, and is a conservative prediction of web cracking for all but the box girders (which are addressed below). 3.8.4 Evaluation of Data for AASHTO BI-36 Test Girder As indicated in the two previous sections, the BI-36 box girder did not satisfy the criterion of the maximum principal tensile stress in the web at the time of first cracking, i.e., the measured principal stress at cracking was less than 0.11√f ′c . Two plausible explanations are provided in the following: The box girder was the only non-composite sections tested. If Eq. 3.9 is rearranged, Eq. 12 is obtained: Eq. 3.12 2 v f f fpc t t( )= + Increasing fpc increases v, which increases the shear force (and the load) that causes cracking. In a non-composite girder, fpc = Ppe/Anc. The other terms are bending terms, which are zero at the neutral axis of non-composite girders. If the value of Ppe is overestimated, the cracking load will be overestimated, or restated, for a given load; overestimating Ppe will underestimate the principal tensile stress in the web. Increasing fpc would also increase Vcw; thus, underestimating the loss of prestressing force would increase the value of Vcw. Using the data from the box girder, a “what if ” analysis was done. In order to obtain the observed cracking load, the prestress losses would have to be between 35% and 50%. This loss is clearly unre- alistic as prestressing force losses are usually 15%–25%, and those values occur after a very long time. The girder was 97 days old when End B was tested, and 105 days old at the time of testing of End A; hence, the losses would be expected to be less than 15%–25%. Table 3.17. Comparison of Vcw to cracking shear and measured maximum shear. Girder End Measured V at Cracking (kips) Calculated Vcw (kips) Measured V at Failure (kips) Calculated Vcw+Vs (kips) AASHTO BI-36 A 106 106 246 205 AASHTO BI-36 B 106 135 278 255 AASHTO BT-54 A 209 127 452 241 AASHTO BT-54 B 256 154 511 291 AASHTO Type III-a A 155 119 311 215 AASHTO Type III-a B 187 132 357 235 AASHTO Type III-b A 171 123 321 219 AASHTO Type III-b B 171 145 383 253 Nebraska NU-1100 A 176 120 375* 316 Nebraska NU-1100 B 196 116 277* 301 Texas U-40 A 286 167 748 433 Texas U-40 B 345 187 532* 474 *Not loaded to failure

experimental research approach, Findings, and associated analytical Simulations 95 A second explanation is that the critical section is in the hollow section of the box, which is 4 in. from the solid end diaphragm. The transition from the solid end diaphragm to the hollow section creates a disturbed region (D region) and the equations for shear and bending stresses do not apply. This hypothesis was examined by comparing the stresses calculated from fundamental mechanics (Mohr’s Circle) to those predicted by the calibrated FEM models. The stresses were computed for three girders: (1) AASHTO BI-36 with end diaphragms, (2) AASHTO Type III-b with a single web, and (3) Texas U-40 that did not have end diaphragms. The results shown in Table 3.18 indicate that the locations of peak stresses from basic principles and FEM analysis are essentially identical, and that basic principles are sufficiently accurate to estimate the peak stresses for the AASHTO Type III-b and Texas U-40 but not the AASHTO BI-36. Basic prin- ciples are based on the Bernoulli beam assumption (i.e., plane sections remain plane), which are not applicable to D regions. For the AASHTO BI-36, the FEM model shows almost twice the stress calculated from basic principles (Mohr’s Circle). In areas within h of concrete end diaphragms, a more exact analysis of the web stresses is needed to obtain appropriate values. Because this is impractical in a design situation, the calcu- lated tensile stress should be limited to 0.08 fc′ ksi under the Service I limit state. Table 3.18. Comparison of stresses at the onset of web cracking. AASHTO BI- 36 AASHTO Type III-b Texas U-40 End A End B End A End B End A End B Applied load (kips) 120 120 200 200 360 440 Peak principal stress (psi) from FEM 687 607 392 435 514 435 Location of peak stress from FEM Near N.A. N.A. N.A. N.A. Approximately @ N.A. Near top flange Stress (psi) from basic principles 323 246 472 407 506 586 Location of peak stress from basic principles N.A. N.A. N.A. N.A. N.A. Top flange/web Stress from basic principles/FEM stress 0.47 0.41 1.20 0.94 0.98 1.35 N.A. = Neutral axis.